Why do launch vehicles use liquid hydrogen as fuel?

You can think about what it's like to burn coal with a rocket!

We say that the basic principle of a rocket is recoil, that is, ejecting gas. If a rocket wants to fly, it must meet a basic condition, that is, the recoil force is greater than gravity, and the recoil force is all obtained by gas injection. According to the momentum theorem, momentum depends on speed and mass, so it is usually necessary to consider the mass of a fuel comprehensively. If a rocket wants to gain enough momentum, it must reach the momentum of reflected gas, and then the rate of injecting gas must be high. Fuel combustion releases its own internal energy, which is released by changing the volume of gas to do work, that is, the gas expands, so that the gas will be ejected outward, and the expansion rate is of course determined by the heat released per unit mass in unit volume time, that is, the specific heat. Besides, rockets need to be as small as possible when launching. In this case, although the combustion value of some fuels is greater than that of hydrogen, their use is limited by quality reasons.

In fact, hydrogen is rarely used as rocket fuel now, and hydrazine, namely N2H4, is more comprehensive.